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Linear & Abstract Algebra

- Vector spaces and linear transformations. Groups and other algebraic structures along with Number Theory.
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Jan16-12 Greg Bernhardt
Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions...
Feb23-13 09:24 AM
micromass
1 35,127
I do not know if this is a common/standard construction, so here is my motivation for this question. From Crystal...
Jul21-11 09:06 AM
kdbnlin78
2 1,731
When chracterizing the definition of unique factorization domain ring, the Hungerford's text, for example, states that...
May9-12 12:18 AM
Sankaku
7 1,731
let be the function given by f(x)=w(x)t^-3mu(x) where mu(x) is the Mobius function and w(x)=Sum(1<n<infinite)d(x-n)...
Sep7-04 08:44 AM
eljose79
4 1,730
So I'm kind of confused about the definition: a-b\in I Why a - b instead of a + b?
Jan27-08 01:44 PM
mathwonk
3 1,730
Hey guys, I need to prove a few theorems about vector spaces using the axioms. a) Prove: if -v = v, then v = 0 ...
Jan27-08 05:19 PM
mathwonk
1 1,730
Hi, Does anyone know how to prove rank(A)=rank(AT A) where A is any matrix and AT is the transposed of matrix A? I...
Jan30-10 05:26 PM
rochfor1
1 1,730
Let u,v,w\in V a vector space over a field F such that u≠v≠w. If { u , v , w } is a basis for V. Prove that { u+v+w ,...
Dec6-11 03:17 PM
Hurkyl
8 1,730
Here a polyform is a plane figure constructed by joining together sides of identical regular polygons - an equilateral...
Jan27-07 08:20 PM
Loren Booda
0 1,729
Given a linear tansformation T of a vector space V (over a field K) with eigenbasis {v_{1},....,v_{n}}, and a...
May16-11 10:45 AM
dward1996
2 1,729
I saw the following problem on my abstract algebra book (dummit && foote) , I tried to solve it but I couldn't : Let...
Oct11-10 04:03 AM
hermanni
3 1,728
The commutator for group theory is =X^{-1}Y^{-1}XY whereas the quantum commutator is =XY-YX . At first glance,...
Apr5-11 07:36 AM
lpetrich
6 1,728
hi all, Which is the fastest algorithm for linear equations in the form of A*X = B. Where A can be a symmetric or...
Feb25-12 10:34 AM
AlephZero
8 1,728
i'm trying to understand the relationship between a matrix and it's adjoint and transpose. i'm trying to develope some...
Oct23-07 11:59 AM
HallsofIvy
1 1,726
"Let p be a prime such that there exists a solution to the congruence x^2\equiv - 2\mod p. THEN there are integers a...
Feb24-10 09:27 PM
robert Ihnot
7 1,726
Let f, g \in \mathbb{Z} be given as follows: f = x^8 + y^8 + z^6 and g = x^3 +y^3 + z^3. Express if possible f and g...
Apr6-10 04:51 AM
Eynstone
3 1,726
sorry im new and posted instead of previewing...im currently writing the post
May16-11 09:26 AM
saulg
2 1,726
I was give the fallowing to prove and i would like it know if anyone thinks i did this right lol.... Let u_1, u_2,...
Sep17-04 12:26 PM
mathwonk
3 1,725
Hi, Let's say I have two points: Pa = (0, 0, -30) Pb = (-2.5, -2.5, 7.5) and I want to find the X and Y...
Jan3-09 10:51 AM
pjhphysics
8 1,725
I was thinking about some similarities in the definitions of group and field, and if it would be possible to...
Dec28-11 01:49 PM
Damidami
8 1,725
I choose a random number p_1 \in and a subsequent series of (increasingly smaller) random numbers p_i \in . Then I...
Feb10-13 09:59 PM
D H
6 1,725
it is possible to evaluate sums over the set of Rational so \sum_{q} f(q) with q= \frac{m}{n} and m and n are...
Mar31-12 06:39 PM
A. Bahat
4 1,724
Dear All, I have a linear system of equations such as Ax = b where A is a m-by-n matrix and m < n and A is a full...
May26-12 07:52 AM
algebrat
1 1,724
So I'm reading a paper which assumes the following statement but I would like to be able to prove it. Let S denote...
Mar19-11 08:25 AM
ihavenoidea
3 1,723
hi.. can anyone say what is the concept behind change of basis.. y do we change a vector of one basis to another?
Apr4-11 05:59 AM
td21
4 1,723
Hi, I have the following \underset{\|\mathbf{x}\|^2=1}{\text{max...
Mar14-12 02:24 AM
S_David
0 1,723
The following interesting result popped up in an old probability textbook (without proof or citations) and I'm curious...
Oct15-10 05:23 PM
bpet
2 1,722
I have about 5 questions all of a similar form ..... \mathbb{F} \cong \mathbb{F} \times \mahbb{F} if 1+1 \neq...
Dec21-07 06:30 AM
morphism
4 1,721
How many symmetries (and what symmetries) and how many elements do the transformation groups of the equilateral...
Dec5-08 05:57 PM
adriank
3 1,721
what are all the ring homomorphism from Z to Z. Thank you
Dec10-09 05:15 PM
esisk
4 1,721
Is it correct to say that any order 4 group is only isomorphic to either C4 or C2+C2 ? where C4 is the order 4...
May23-12 03:10 PM
lpetrich
3 1,721
Mr X catches 7000 fish appox from a sea.When he lines up the fish in rows of 9 three remain. These three fish are...
Jan24-09 06:17 AM
wsalem
1 1,720
I want to show that the set of points (p,q) on the plane with rational coordinates p and q is countable. I proved set...
Jun20-09 04:41 PM
HallsofIvy
2 1,720
think i have discovered an integral equation for the Xi-function \Xi (z)= A\int_{-\infty}^{\infty} \phi...
Nov17-09 09:19 AM
zetafunction
1 1,720
This is a question in my textbook: "The hyperplanes H1 and H2 have dimensions p and q, respectively. What is the...
Aug6-08 11:48 AM
JG89
5 1,719
Hi, folks I have had a hard time to find out whether or not there is a theorem in Linear Algebra or Spectral Theory...
Jun10-14 09:52 PM
Haborix
5 1,719
Someone, please help me solve this problem: First if R is a ring and * is an involution, then U(R, *):= {x \in...
Apr10-08 04:55 PM
Mechmathian
6 1,718
I think I have worked out a formula for Prime Numbers. I said, "I think," because 1. I dont know , Is that formula...
Apr15-10 12:30 PM
CRGreathouse
7 1,718
Im struggling to find proof for this suspicion I have; Given is a function f(t) and a normalised function h(t), and...
Nov24-10 10:22 AM
gerben
3 1,717
Hi Everyone, I am kind of looking some online text to understand Lie Algebra, Group Theory and so forth. I usually...
Mar27-12 08:39 PM
chiro
9 1,717
Suppose I have a matrix that looks like this 2.415212e-09 9.748863e-10 -2.415212e-09...
Apr25-12 03:21 AM
FoldHellmuth
3 1,717

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